A study used random samples to survey the political affiliations of cell-only and landline users under 30. The study found 49% of cell-only users identified as Democrat compared to 47% of landline users. A chi-squared test was conducted to determine if phone type and political affiliation were related. The test found a p-value of 0.199897, above the standard significance level. Therefore, there is insufficient evidence to conclude that phone type and political affiliation are related for this age group.

1. Practice Problem
Chi-Squared Test for Homogeneity

2.  Opinion polls used to exclude cell phones from their
random digit dialing. If the opinions of people with cell
phones differ from those people who have landlines, then
the poll may not represent the entire population. A group
of people got together and interviewed separate random
samples of cell-only and landline telephone users who
were less than 30 years old. Do we have sufficient
evidence to suggest that the opinion of cell phone users
differ from landline users?
Cell-Only Sample Landline Sample
Democrat 49 47
Independent 15 27
Republican 32 30

3. Take a few minutes to
work this problem on your
own sheet of paper and
then flip through this
slideshow in order to
check your work!

4. Hypotheses
 H0: There is no difference in which type of phone is sampled and the political
affiliation for people under 30 years old.
 Ha: There is a difference in which type of phone is sampled and the political
affiliation for people under 30 years old.

5. Check conditions:
 Random – it was stated in the problem that they interviewed separate random
samples.
 Large Sample Size – need to check expected counts to make sure they are all
at least 5.
 EXPECTED COUNTS:
Cell-Only Sample Landline Sample
Democrat 46.08 49.92
Independent 20.16 21.84
Republican 29.76 32.24

6. Do the math!
 𝜒2
=
(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑−𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑)2
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑
 𝜒2 =
(49−46.08)2
46.08
+
(47−49.92)2
49.92
+ ⋯
(30−32.24)2
32.24
= 3.2199
 df: 2
 P-value: 0.199897

7. State conclusion!
 Since the p-value is so large, we do not have enough evidence to reject the
null hypothesis.
 There is no difference in which type of phone is sampled and the political
affiliation for people under 30 years old.